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Sorry this may be an obvious one...can anyone help me with getting from the first to the second equation below? I'm particularly stuck with manipulating the terms inside the summations formulas.

I can derive to here:

[tex]

\sum_{i=1}^{N}x_iy_i - N\bar{x}\bar{y} - \left( \sum_{i=1}^{N}x_i^2 - N\bar{x}^2\right)b_2 = 0

[/tex]

But am a bit unsure of the exact manipulation to get to here:

[tex]

b_2 = \frac{\sum_{i=1}^{N}(x_i-y_i)(y_i-\bar{y})}{\sum_{i=1}^{N}(x_i-\bar{x})^2}

[/tex]

Thanks in advance!

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# Deriving Regression Coefficients

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